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I have a time series of monthly data that is 40 observations ($3\frac{1}{3}$ seasonal cycles) long. HEGY test and CH test give contradicting results w.r.t. presence of a seasonal unit root. HEGY test gives that series have seasonal unit roots while CH test gives that all the series do not have seasonal unit roots.

  1. Since my sample size is small, which test has the highest power?
  2. Due to the relative short sample size, seasonal differencing would cause a significant fraction of observations to get removed. Can I go with CH test results?
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    $\begingroup$ I have edited the post extensively. Feel free to revert back if you think I have misrepresented anything. $\endgroup$ Jan 22, 2022 at 14:07
  • $\begingroup$ @RichardHardy Thank you so much! The question sounds much clear now. Exactly what I wanted to ask. $\endgroup$
    – Geek_Tech
    Jan 22, 2022 at 14:28
  • $\begingroup$ @RichardHardy link this paper mentions that HEGY has low power when it comes to small sample sizes. However I couldn't find evidence regarding the power of CH test when it comes to small samples. $\endgroup$
    – Geek_Tech
    Jan 22, 2022 at 14:40
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    $\begingroup$ I do not think there is a way around the small sample size. This is a very fundamental problem. All tests will have low power on such data. $\endgroup$ Jan 22, 2022 at 14:44
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    $\begingroup$ (I could perhaps clarify in this context my earlier request of visualizations. I thought your 40-long time series was quarterly. That is long enough for trying to visually assess presence of a seasonal unit root. Once I learned it was monthly, my view changed.) $\endgroup$ Jan 22, 2022 at 21:58

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